## Abstract

We consider linear mapping functions for physical layer network coding (PNC), using a generalised description of linear mapping on some arbitrary algebraic structure. We show that a ring is a sufficient structure for this purpose, and consider the requirements for the coefficients used in the linear functions. We consider both rings based on integers and rings based on binary matrices. We then consider the performance of the mappings in the two-way relay channel using QPSK as an example, and evaluate the information loss in terms of the equivocation at the destination as a function of the relative fading of the two channels. Hence we determine the outage probability of the schemes.

Original language | English |
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Title of host publication | 20th European Wireless Conference, EW 2014 |

Publisher | VDE VERLAG GMBH |

Pages | 757-762 |

Number of pages | 6 |

ISBN (Electronic) | 9783800736218 |

Publication status | Published - 2014 |

Event | 20th European Wireless Conference, EW 2014 - Barcelona, Spain Duration: 14 May 2014 → 16 May 2014 |

### Publication series

Name | 20th European Wireless Conference, EW 2014 |
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### Conference

Conference | 20th European Wireless Conference, EW 2014 |
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Country/Territory | Spain |

City | Barcelona |

Period | 14/05/14 → 16/05/14 |

### Bibliographical note

Publisher Copyright:© VDE VERLAG GMBH, Berlin, Offenbach, Germany.

## Keywords

- Fields
- Linear mapping
- Physical layer network coding
- PNC
- Rings